Answer
$51.5mol\ NO_{2}$
Work Step by Step
$2.78kg\ N_{2}O_{5}\times\frac{1000g}{1kg}\times \frac{1mol\ N_{2}O_{5}}{108.01g\ N_{2}O_{5}}\times\frac{4mol\ NO_{2}}{2mol\ N_{2}O_{5}} = 51.5mol\ NO_{2}$
To calculate the number of moles formed, multiply the number of moles reacted with the mole ratio obtained using the balanced chemical equation.
Remember to state your answer using the correct number of significant figures.